Given a string S which contains only digit-characters. How many subsequences can be obtained from S such that every digit is strictly greater than all previous digits in that subsequence.
As for example if S=7598 then there are 8 subsequences which follow the above constraint. These are 7,5,9,8,79,78,59,58. Notice that 7598 is not a required subsequence because 7>5 and 9>8.

Note: A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Input

Input starts with an integer T (≤ 1000), denoting the number of test cases. Each case contains a string S. The length of S does not exceed 10000. S does not contain any leading zeros.

Output

For each case, print the a string(without quotes) "Case i: " follwed by number of subsequences where "i" is test case number. Answer may be very large, so output it modulo 10^9+7.

Example

Input:
2
4
7598
Output:
Case 1: 1
Case 2: 8
For small constraints: www.spoj.com/problems/SUBP/